GREEN BAY, Wis. — The ball popped loose from Green Bay running back James Starks’s grasp Sunday night after he made a catch with less than three minutes to play and the Packers leading by a touchdown. For the briefest of moments, Giants wide receiver Odell Beckham Jr. and Coach Ben McAdoo thought another frustrating night for the offense might be salvaged.

“We saw him cough the ball up, and we might have a chance to go down and tie it up,” said Beckham, who had caught his first touchdown pass of the season moments before. “I was very excited.”

But Starks, in a pile of players, recovered the fumble. Packers quarterback Aaron Rodgers then converted a third-and-10 on the next play with a 13-yard pass to Randall Cobb, and that was that. The Packers ran out the clock as the Giants lost their third consecutive game, 23-16.

Both teams were missing critical players in the defensive secondary, but an expected passing duel between Rodgers and Eli Manning failed to materialize.

An unexceptional Rodgers threw for 259 yards, two touchdowns and two interceptions at Lambeau Field, while Manning struggled for the second consecutive week. Manning was 11-for-26 early in the fourth quarter before driving the Giants to their only touchdown, Beckham’s 8-yard catch with 2 minutes 54 seconds to play. Manning finished 18-for-35 for 199 yards.

“We need to block better,” McAdoo said. “We need to make better throws. And we need to make contested plays.”

Beckham, the Giants’ enigmatic wide receiver, avoided penalties and controversy while catching five passes for 56 yards, one week after recording a career-low 23 receiving yards. And the Giants’ defense nabbed its first takeaways of the season with two interceptions by Janoris Jenkins in the first half.

But McAdoo’s return to Green Bay, where he served as an assistant to Packers Coach Mike McCarthy for eight seasons, proved unsatisfying, with the Packers (3-1) outgaining the Giants 406 yards to 213. Eddie Lacy rushed for 81 yards on 11 carries before leaving with an ankle injury, outgaining the Giants (2-3) on the ground by himself; the Giants ran 15 times for 43 yards.

“We’ve just got to do more,” Beckham said. “We’ve got to sustain drives, be more than one-dimensional. They came out with a game plan and stuck to it.”

Manning failed to exploit a Green Bay secondary that was missing the starting cornerbacks Sam Shields and Damarious Randall. (Shields had a concussion, and Randall had a groin injury.) Filling in were the second-year pros Quinten Rollins, who made four starts last year, and LaDarius Gunter, an undrafted free agent. McAdoo said the Packers played so much zone, keeping two safeties deep, that the opportunity for one-on-one matchups was not there.

“I don’t know if it’s we’re not clicking,” Manning said. “Last week we went up against a really good defense in Minnesota, and this week, again, against a good defense. I still feel we’re a good offense. We have to understand how teams are going to start playing us. We have to be ready for that and just try to get them out of it.”

The Giants fell behind before Manning ever touched the ball. Rodgers mixed runs and rollout passes on his first drive, taking more than eight minutes off the clock before finding a diving Jordy Nelson in the end zone for a 2-yard touchdown.

The Giants failed to move the ball on their opening drive, and Green Bay appeared to go up by 14-0 when Rodgers threw 21 yards to Cobb in the end zone on a quick post pattern. But offsetting penalties negated the play, and a pass to Nelson bounced off his hands and right to Jenkins.

Josh Brown kicked the first of his three field goals, a 47-yarder, in the second quarter for the Giants’ first points.

Green Bay continued to move the ball at will, however, especially on the ground.

Lacy’s 31-yard burst through the left side brought the Packers from their 20-yard line to the Giants’ 49. Four plays later, Rodgers lofted a pass over cornerback Michael Hunter to Davante Adams. Hunter tried to shove Adams out of bounds, but Adams switched the ball to his left hand and slipped it around the pylon for a 29-yard touchdown and a 14-3 lead.

Jenkins’s second interception gave the Giants the ball at the Packers’ 40. Manning threw behind Sterling Shepard on third down, the ball hitting safety Micah Hyde in the shoulder, and Brown then converted from 41 yards.

Late in the half Manning could not connect with tight end Will Tye, who was wide open over the middle, the ball glancing high off Tye’s fingers. Then Manning fumbled while being sacked by Kyler Fackrell, with Kenny Clark recovering the ball for Green Bay on the Giants’ 31 with 1:15 left.

There, the Giants caught a break: an offensive pass interference penalty on Adams for grabbing Trevin Wade’s jersey as they jostled on the route. Instead of a possible touchdown, Mason Crosby’s 44-yard field goal put Green Bay up by 17-6 at the half.

McAdoo worked in Green Bay for McCarthy from 2006 to 2013, coaching tight ends for six seasons and quarterbacks for two before joining Tom Coughlin’s staff as the Giants’ offensive coordinator.

Last week McAdoo said he had no special feelings about coaching against his former boss in one of the N.F.L.’s most storied stadiums. How, he asked, could he expect his players to be disciplined and poised if he could not be that way himself?

Poised or not, in the end, the Giants could not make enough plays.

“It would have been nice to get a stop at the end,” McAdoo said. “It would have been nice to come up with the ball, too. There were a lot of bodies in there scrapping for the ball, but they came up with it.”

A version of this article appears in print on , on Page D6 of the New York edition with the headline: Unexceptional Packers Offense Is Good Enough to Beat Giants. Order Reprints | Today’s Paper | Subscribe